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That was not the question. The question was what is mathematics. There is an entire branch of math (arguably, the lion's share) that is entirely abstract.

The question of justifying whether is matters (and to whom) is a different animal. That becomes a matter of whether you think it matters, as compared to those who make a living from it, and those to pay them to make a living from it.

Granted, it is certainly true that the more we learn due to abstract mathematics, the more we find we can apply it to the real world, but that is not at all the same thing as saying mathematics is applied math. The abstract math comes first; it may lead to applications.

That was not the question. The question was what is mathematics. There is an entire branch of math (arguably, the lion's share) that is entirely abstract.

The question of justifying whether is matters (and to whom) is a different animal. That becomes a matter of whether you think it matters, as compared to those who make a living from it, and those to pay them to make a living from it.

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Mathematics predicted the existence of the Higgs boson. Not a useless discovery. It warranted a Nobel prize.

The understanding of material particles lead to the prediction of the Higgs boson .

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Yes, lets just throw a bunch of particle together and presto. C'mon river, it took some 30 years of theoretical and applied mathematics to build the Cern collider which could physically be used to create a Higgs boson. And it did.

Yes, lets just throw a bunch of particle together and presto. C'mon river, it took some 30 years of theoretical and applied mathematics to build the Cern collider which could physically be used to create a Higgs boson. And it did.

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Create a Higgs boson .

Look , I thought that this collider had no chance of discovering a new particle , I was wrong . I have no problem with being wrong , really I don't .

But , when investigating ZPF ( zero point field ) is it really all that surprising , that the Higgs boson particle was found ?

Look , I thought that this collider had no chance of discovering a new particle , I was wrong . I have no problem with being wrong , really I don't .

But , when investigating ZPF ( zero point field ) is it really all that surprising , that the Higgs boson particle was found ?

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I have been proven wrong many times, but IMO, if accompanied by a clear narrative why my assumption was wrong, that only leads to greater understanding. And that is my single aim.
I am here to learn, not to lecture about things outside of my expertise.

The main point is that mathematics predicted the existence of a particle, which no one knew even existed.
This also suggests that a fundamental aspect of the universe is a Higgs field, which is a major part of understanding how particles acquire mass and must travel @ sub-luminal speeds

The Higgs field is an energy field that is thought to exist everywhere in the universe. The field is accompanied by a fundamental particle called the Higgs boson, which the field uses to continuously interact with other particles. As particles pass through the field they are "given" mass and, similar to an object passing through treacle (or molasses), will become slower, and cannot travel at the speed of light because they have mass.

I have been proven wrong many times, but IMO, if accompanied by a clear narrative why my assumption was wrong, that only leads to greater understanding. And that is my single aim.
I am here to learn, not to lecture about things outside of my expertise.

The main point is that mathematics predicted the existence of a particle, which no one knew even existed.
This also suggests that a fundamental aspect of the universe is a Higgs field, which is a major part of understanding how particles acquire mass and must travel @ sub-luminal speedshttps://simple.wikipedia.org/wiki/Higgs_field.

Zero-point energy (ZPE) or ground state energy is the lowest possible energy that a quantum mechanical system may have. Unlike in classical mechanics, quantum systems constantly fluctuate in their lowest energy state due to the Heisenberg uncertainty principle.[1] As well as atoms and molecules, the empty space of the vacuum has these properties. According to Quantum Field Theory the universe can be thought of not as isolated particles but continuous fluctuating fields: matter fields, whose quanta are fermions (i.e. leptons and quarks), and force fields, whose quanta are bosons (e.g. photons and gluons). All these fields have zero-point energy.